We show that the Brownian continuum random tree is the Gromov–Hausdorff–Prohorov scaling limit of the uniform spanning tree on high-dimensional graphs including the d-dimensional torus \({\mathbb {Z}}_n^d\) with \(d>4\), the hypercube \(\{0,1\}^n\), and transitive expander graphs. Several corollaries for associated quantities are then deduced: convergence in distribution of the rescaled diameter, height and simple random walk on these uniform spanning trees to their continuum analogues on the continuum random tree.

中文翻译：

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高维均匀生成树的GHP缩放极限

我们证明布朗连续随机树是高维图上均匀生成树的 Gromov–Hausdorff–Prohorov 缩放极限，包括d维环面\({\mathbb {Z}}_n^d\)和\( d>4\)、超立方体\(\{0,1\}^n\)和传递扩展图。然后推导出相关量的几个推论：这些均匀生成树上的重新缩放的直径、高度和简单随机游走的分布收敛到连续统随机树上的连续统类似物。